We investigate cooling mechanisms in magneto-optically and magnetically trapped erbium. We find efficient sub-Doppler cooling in our trap, which can persist even in large magnetic fields due to the near degeneracy of two Lande g factors. Furthermore, a continuously loaded magnetic trap is demonstrated where we observe temperatures below 25 υK. These favorable cooling and trapping properties suggest a number of scientific possibilities for rare-earth-metal atomic physics, including narrow linewidth laser cooling and spectroscopy, unique collision studies, and degenerate bosonic and fermionic gases with long-range magnetic dipole coupling.